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Article ; Online: Multiple imputation strategies for missing event times in a multi-state model analysis.

Curnow, Elinor / Hughes, Rachael A / Birnie, Kate / Tilling, Kate / Crowther, Michael J

2024 Volume 43, Issue 6, Page(s) 1238–1255

Abstract: In clinical studies, multi-state model (MSM) analysis is often used to describe the sequence of events that patients experience, enabling better understanding of disease progression. A complicating factor in many MSM studies is that the exact event times ...

Abstract	In clinical studies, multi-state model (MSM) analysis is often used to describe the sequence of events that patients experience, enabling better understanding of disease progression. A complicating factor in many MSM studies is that the exact event times may not be known. Motivated by a real dataset of patients who received stem cell transplants, we considered the setting in which some event times were exactly observed and some were missing. In our setting, there was little information about the time intervals in which the missing event times occurred and missingness depended on the event type, given the analysis model covariates. These additional challenges limited the usefulness of some missing data methods (maximum likelihood, complete case analysis, and inverse probability weighting). We show that multiple imputation (MI) of event times can perform well in this setting. MI is a flexible method that can be used with any complete data analysis model. Through an extensive simulation study, we show that MI by predictive mean matching (PMM), in which sampling is from a set of observed times without reliance on a specific parametric distribution, has little bias when event times are missing at random, conditional on the observed data. Applying PMM separately for each sub-group of patients with a different pathway through the MSM tends to further reduce bias and improve precision. We recommend MI using PMM methods when performing MSM analysis with Markov models and partially observed event times.
MeSH term(s)	Humans ; Data Interpretation, Statistical ; Computer Simulation ; Probability ; Research Design ; Bias
Language	English
Publishing date	2024-01-22
Publishing country	England
Document type	Journal Article
ZDB-ID	843037-8
ISSN	1097-0258 ; 0277-6715
ISSN (online)	1097-0258
ISSN	0277-6715
DOI	10.1002/sim.10011
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Article ; Online: INTEREST: INteractive Tool for Exploring REsults from Simulation sTudies.

Gasparini, Alessandro / Morris, Tim P / Crowther, Michael J

Journal of data science, statistics, and visualisation

2022 Volume 1, Issue 4

Abstract: Simulation studies allow us to explore the properties of statistical methods. They provide a powerful tool with a multiplicity of aims; among others: evaluating and comparing new or existing statistical methods, assessing violations of modelling ... ...

Abstract	Simulation studies allow us to explore the properties of statistical methods. They provide a powerful tool with a multiplicity of aims; among others: evaluating and comparing new or existing statistical methods, assessing violations of modelling assumptions, helping with the understanding of statistical concepts, and supporting the design of clinical trials. The increased availability of powerful computational tools and usable software has contributed to the rise of simulation studies in the current literature. However, simulation studies involve increasingly complex designs, making it difficult to provide all relevant results clearly. Dissemination of results plays a focal role in simulation studies: it can drive applied analysts to use methods that have been shown to perform well in their settings, guide researchers to develop new methods in a promising direction, and provide insights into less established methods. It is crucial that we can digest relevant results of simulation studies. Therefore, we developed
Language	English
Publishing date	2022-01-25
Publishing country	Netherlands
Document type	Journal Article
ISSN	2773-0689
ISSN (online)	2773-0689
DOI	10.52933/jdssv.v1i4.9
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Article ; Online: A flexible parametric accelerated failure time model and the extension to time-dependent acceleration factors.

Crowther, Michael J / Royston, Patrick / Clements, Mark

Biostatistics (Oxford, England)

2022 Volume 24, Issue 3, Page(s) 811–831

Abstract: Accelerated failure time (AFT) models are used widely in medical research, though to a much lesser extent than proportional hazards models. In an AFT model, the effect of covariates act to accelerate or decelerate the time to event of interest, that is, ... ...

Abstract	Accelerated failure time (AFT) models are used widely in medical research, though to a much lesser extent than proportional hazards models. In an AFT model, the effect of covariates act to accelerate or decelerate the time to event of interest, that is, shorten or extend the time to event. Commonly used parametric AFT models are limited in the underlying shapes that they can capture. In this article, we propose a general parametric AFT model, and in particular concentrate on using restricted cubic splines to model the baseline to provide substantial flexibility. We then extend the model to accommodate time-dependent acceleration factors. Delayed entry is also allowed, and hence, time-dependent covariates. We evaluate the proposed model through simulation, showing substantial improvements compared to standard parametric AFT models. We also show analytically and through simulations that the AFT models are collapsible, suggesting that this model class will be well suited to causal inference. We illustrate the methods with a data set of patients with breast cancer. Finally, we provide highly efficient, user-friendly Stata, and R software packages.
MeSH term(s)	Humans ; Female ; Survival Analysis ; Proportional Hazards Models ; Computer Simulation ; Time Factors ; Breast Neoplasms ; Models, Statistical
Language	English
Publishing date	2022-05-25
Publishing country	England
Document type	Journal Article
ZDB-ID	2031500-4
ISSN	1468-4357 ; 1465-4644
ISSN (online)	1468-4357
ISSN	1465-4644
DOI	10.1093/biostatistics/kxac009
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Article ; Online: Exploring different research questions via complex multi-state models when using registry-based repeated prescriptions of antidepressants in women with breast cancer and a matched population comparison group.

Skourlis, Nikolaos / Crowther, Michael J / Andersson, Therese M-L / Lu, Donghao / Lambe, Mats / Lambert, Paul C

BMC medical research methodology

2023 Volume 23, Issue 1, Page(s) 87

Abstract: Background: Multi-state models are used to study several clinically meaningful research questions. Depending on the research question of interest and the information contained in the data, different multi-state structures and modelling choices can be ... ...

Abstract	Background: Multi-state models are used to study several clinically meaningful research questions. Depending on the research question of interest and the information contained in the data, different multi-state structures and modelling choices can be applied. We aim to explore different research questions using a series of multi-state models of increasing complexity when studying repeated prescriptions data, while also evaluating different modelling choices. Methods: We develop a series of research questions regarding the probability of being under antidepressant medication across time using multi-state models, among Swedish women diagnosed with breast cancer (n = 18,313) and an age-matched population comparison group of cancer-free women (n = 92,454) using a register-based database (Breast Cancer Data Base Sweden 2.0). Research questions were formulated ranging from simple to more composite ones. Depending on the research question, multi-state models were built with structures ranging from simpler ones, like single-event survival analysis and competing risks, up to complex bidirectional and recurrent multi-state structures that take into account the recurring start and stop of medication. We also investigate modelling choices, such as choosing a time-scale for the transition rates and borrowing information across transitions. Results: Each structure has its own utility and answers a specific research question. However, the more complex structures (bidirectional, recurrent) enable accounting for the intermittent nature of prescribed medication data. These structures deliver estimates of the probability of being under medication and total time spent under medication over the follow-up period. Sensitivity analyses over different definitions of the medication cycle and different choices of timescale when modelling the transition intensity rates show that the estimates of total probabilities of being in a medication cycle over follow-up derived from the complex structures are quite stable. Conclusions: Each research question requires the definition of an appropriate multi-state structure, with more composite ones requiring such an increase in the complexity of the multi-state structure. When a research question is related with an outcome of interest that repeatedly changes over time, such as the medication status based on prescribed medication, the use of novel multi-state models of adequate complexity coupled with sensible modelling choices can successfully address composite, more realistic research questions.
MeSH term(s)	Humans ; Female ; Breast Neoplasms/drug therapy ; Neoplasm Recurrence, Local ; Antidepressive Agents/therapeutic use ; Registries ; Drug Prescriptions
Chemical Substances	Antidepressive Agents
Language	English
Publishing date	2023-04-10
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2041362-2
ISSN	1471-2288 ; 1471-2288
ISSN (online)	1471-2288
ISSN	1471-2288
DOI	10.1186/s12874-023-01905-9
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Article ; Online: Modeling the multi-state natural history of rare diseases with heterogeneous individual patient data: A simulation study.

Broomfield, Jonathan / Abrams, Keith R / Freeman, Suzanne / Latimer, Nicholas / Rutherford, Mark J / Crowther, Michael J

Statistics in medicine

2023 Volume 43, Issue 1, Page(s) 184–200

Abstract: Multi-state survival models are used to represent the natural history of a disease, forming the basis of a health technology assessment comparing a novel treatment to current practice. Constructing such models for rare diseases is problematic, since ... ...

Abstract	Multi-state survival models are used to represent the natural history of a disease, forming the basis of a health technology assessment comparing a novel treatment to current practice. Constructing such models for rare diseases is problematic, since evidence sources are typically much sparser and more heterogeneous. This simulation study investigated different one-stage and two-stage approaches to meta-analyzing individual patient data (IPD) in a multi-state survival setting when the number and size of studies being meta-analyzed are small. The objective was to assess methods of different complexity to see when they are accurate, when they are inaccurate and when they struggle to converge due to the sparsity of data. Biologically plausible multi-state IPD were simulated from study- and transition-specific hazard functions. One-stage frailty and two-stage stratified models were estimated, and compared to a base case model that did not account for study heterogeneity. Convergence and the bias/coverage of population-level transition probabilities to, and lengths of stay in, each state were used to assess model performance. A real-world application to Duchenne Muscular Dystrophy, a neuromuscular rare disease, was conducted, and a software demonstration is provided. Models not accounting for study heterogeneity were consistently out-performed by two-stage models. Frailty models struggled to converge, particularly in scenarios of low heterogeneity, and predictions from models that did converge were also subject to bias. Stratified models may be better suited to meta-analyzing disparate sources of IPD in rare disease natural history/economic modeling, as they converge more consistently and produce less biased predictions of lengths of stay.
MeSH term(s)	Humans ; Models, Statistical ; Rare Diseases/epidemiology ; Frailty ; Computer Simulation ; Software
Language	English
Publishing date	2023-11-06
Publishing country	England
Document type	Journal Article
ZDB-ID	843037-8
ISSN	1097-0258 ; 0277-6715
ISSN (online)	1097-0258
ISSN	0277-6715
DOI	10.1002/sim.9949
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Article ; Online: Relaxing the assumption of constant transition rates in a multi-state model in hospital epidemiology.

Hill, Micki / Lambert, Paul C / Crowther, Michael J

BMC medical research methodology

2021 Volume 21, Issue 1, Page(s) 16

Abstract: Background: Multi-state models are being increasingly used to capture complex disease pathways. The convenient formula of the exponential multi-state model can facilitate a quick and accessible understanding of the data. However, assuming time constant ... ...

Abstract	Background: Multi-state models are being increasingly used to capture complex disease pathways. The convenient formula of the exponential multi-state model can facilitate a quick and accessible understanding of the data. However, assuming time constant transition rates is not always plausible. On the other hand, obtaining predictions from a fitted model with time-dependent transitions can be challenging. One proposed solution is to utilise a general simulation algorithm to calculate predictions from a fitted multi-state model. Methods: Predictions obtained from an exponential multi-state model were compared to those obtained from two different parametric models and to non-parametric Aalen-Johansen estimates. The first comparative approach fitted a multi-state model with transition-specific distributions, chosen separately based on the Akaike Information Criterion. The second approach was a Royston-Parmar multi-state model with 4 degrees of freedom, which was chosen as a reference model flexible enough to capture complex hazard shapes. All quantities were obtained analytically for the exponential and Aalen-Johansen approaches. The transition rates for the two comparative approaches were also obtained analytically, while all other quantities were obtained from the fitted models via a general simulation algorithm. Metrics investigated were: transition probabilities, attributable mortality (AM), population attributable fraction (PAF) and expected length of stay. This work was performed on previously analysed hospital acquired infection (HAI) data. By definition, a HAI takes three days to develop and therefore selected metrics were also predicted from time 3 (delayed entry). Results: Despite clear deviations from the constant transition rates assumption, the empirical estimates of the transition probabilities were approximated reasonably well by the exponential model. However, functions of the transition probabilities, e.g. AM and PAF, were not well approximated and the comparative models offered considerable improvements for these metrics. They also provided consistent predictions with the empirical estimates in the case of delayed entry time, unlike the exponential model. Conclusion: We conclude that methods and software are readily available for obtaining predictions from multi-state models that do not assume constant transition rates. The multistate package in Stata facilitates a range of predictions with confidence intervals, which can provide a more comprehensive understanding of the data. User-friendly code is provided.
MeSH term(s)	Hospitals ; Humans ; Markov Chains ; Models, Statistical ; Probability ; Survival Analysis
Language	English
Publishing date	2021-01-11
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ISSN	1471-2288
ISSN (online)	1471-2288
DOI	10.1186/s12874-020-01192-8
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Article ; Online: A scoping methodological review of simulation studies comparing statistical and machine learning approaches to risk prediction for time-to-event data.

Smith, Hayley / Sweeting, Michael / Morris, Tim / Crowther, Michael J

Diagnostic and prognostic research

2022 Volume 6, Issue 1, Page(s) 10

Abstract: Background: There is substantial interest in the adaptation and application of so-called machine learning approaches to prognostic modelling of censored time-to-event data. These methods must be compared and evaluated against existing methods in a ... ...

Abstract	Background: There is substantial interest in the adaptation and application of so-called machine learning approaches to prognostic modelling of censored time-to-event data. These methods must be compared and evaluated against existing methods in a variety of scenarios to determine their predictive performance. A scoping review of how machine learning methods have been compared to traditional survival models is important to identify the comparisons that have been made and issues where they are lacking, biased towards one approach or misleading. Methods: We conducted a scoping review of research articles published between 1 January 2000 and 2 December 2020 using PubMed. Eligible articles were those that used simulation studies to compare statistical and machine learning methods for risk prediction with a time-to-event outcome in a medical/healthcare setting. We focus on data-generating mechanisms (DGMs), the methods that have been compared, the estimands of the simulation studies, and the performance measures used to evaluate them. Results: A total of ten articles were identified as eligible for the review. Six of the articles evaluated a method that was developed by the authors, four of which were machine learning methods, and the results almost always stated that this developed method's performance was equivalent to or better than the other methods compared. Comparisons were often biased towards the novel approach, with the majority only comparing against a basic Cox proportional hazards model, and in scenarios where it is clear it would not perform well. In many of the articles reviewed, key information was unclear, such as the number of simulation repetitions and how performance measures were calculated. Conclusion: It is vital that method comparisons are unbiased and comprehensive, and this should be the goal even if realising it is difficult. Fully assessing how newly developed methods perform and how they compare to a variety of traditional statistical methods for prognostic modelling is imperative as these methods are already being applied in clinical contexts. Evaluations of the performance and usefulness of recently developed methods for risk prediction should be continued and reporting standards improved as these methods become increasingly popular.
Language	English
Publishing date	2022-06-02
Publishing country	England
Document type	Journal Article ; Review
ISSN	2397-7523
ISSN (online)	2397-7523
DOI	10.1186/s41512-022-00124-y
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Article ; Online: On the choice of timescale for other cause mortality in a competing risk setting using flexible parametric survival models.

Skourlis, Nikolaos / Crowther, Michael J / Andersson, Therese M-L / Lambert, Paul C

Biometrical journal. Biometrische Zeitschrift

2022 Volume 64, Issue 7, Page(s) 1161–1177

Abstract: In competing risks settings where the events are death due to cancer and death due to other causes, it is common practice to use time since diagnosis as the timescale for all competing events. However, attained age has been proposed as a more natural ... ...

Abstract	In competing risks settings where the events are death due to cancer and death due to other causes, it is common practice to use time since diagnosis as the timescale for all competing events. However, attained age has been proposed as a more natural choice of timescale for modeling other cause mortality. We examine the choice of using time since diagnosis versus attained age as the timescale when modeling other cause mortality, assuming that the hazard rate is a function of attained age, and how this choice can influence the cumulative incidence functions (
MeSH term(s)	Bias ; Computer Simulation ; Incidence ; Proportional Hazards Models ; Regression Analysis ; Risk Assessment
Language	English
Publishing date	2022-06-16
Publishing country	Germany
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	131640-0
ISSN	1521-4036 ; 0323-3847 ; 0006-3452
ISSN (online)	1521-4036
ISSN	0323-3847 ; 0006-3452
DOI	10.1002/bimj.202100254
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Article ; Online: Development of a dynamic interactive web tool to enhance understanding of multi-state model analyses: MSMplus.

Skourlis, Nikolaos / Crowther, Michael J / Andersson, Therese M-L / Lambert, Paul C

BMC medical research methodology

2021 Volume 21, Issue 1, Page(s) 262

Abstract: Background: Multi-state models are used in complex disease pathways to describe a process where an individual moves from one state to the next, taking into account competing states during each transition. In a multi-state setting, there are various ... ...

Abstract	Background: Multi-state models are used in complex disease pathways to describe a process where an individual moves from one state to the next, taking into account competing states during each transition. In a multi-state setting, there are various measures to be estimated that are of great epidemiological importance. However, increased complexity of the multi-state setting and predictions over time for individuals with different covariate patterns may lead to increased difficulty in communicating the estimated measures. The need for easy and meaningful communication of the analysis results motivated the development of a web tool to address these issues. Results: MSMplus is a publicly available web tool, developed via the Shiny R package, with the aim of enhancing the understanding of multi-state model analyses results. The results from any multi-state model analysis are uploaded to the application in a pre-specified format. Through a variety of user-tailored interactive graphs, the application contributes to an improvement in communication, reporting and interpretation of multi-state analysis results as well as comparison between different approaches. The predicted measures that can be supported by MSMplus include, among others, the transition probabilities, the transition intensity rates, the length of stay in each state, the probability of ever visiting a state and user defined measures. Representation of differences, ratios and confidence intervals of the aforementioned measures are also supported. MSMplus is a useful tool that enhances communication and understanding of multi-state model analyses results. Conclusions: Further use and development of web tools should be encouraged in the future as a means to communicate scientific research.
MeSH term(s)	Humans ; Probability
Language	English
Publishing date	2021-11-27
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2041362-2
ISSN	1471-2288 ; 1471-2288
ISSN (online)	1471-2288
ISSN	1471-2288
DOI	10.1186/s12874-021-01420-9
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Article ; Online: Parametric multistate survival models: Flexible modelling allowing transition-specific distributions with application to estimating clinically useful measures of effect differences.

Crowther, Michael J / Lambert, Paul C

Statistics in medicine

2017 Volume 36, Issue 29, Page(s) 4719–4742

Abstract: Multistate models are increasingly being used to model complex disease profiles. By modelling transitions between disease states, accounting for competing events at each transition, we can gain a much richer understanding of patient trajectories and how ... ...

Abstract	Multistate models are increasingly being used to model complex disease profiles. By modelling transitions between disease states, accounting for competing events at each transition, we can gain a much richer understanding of patient trajectories and how risk factors impact over the entire disease pathway. In this article, we concentrate on parametric multistate models, both Markov and semi-Markov, and develop a flexible framework where each transition can be specified by a variety of parametric models including exponential, Weibull, Gompertz, Royston-Parmar proportional hazards models or log-logistic, log-normal, generalised gamma accelerated failure time models, possibly sharing parameters across transitions. We also extend the framework to allow time-dependent effects. We then use an efficient and generalisable simulation method to calculate transition probabilities from any fitted multistate model, and show how it facilitates the simple calculation of clinically useful measures, such as expected length of stay in each state, and differences and ratios of proportion within each state as a function of time, for specific covariate patterns. We illustrate our methods using a dataset of patients with primary breast cancer. User-friendly Stata software is provided.
MeSH term(s)	Breast Neoplasms/mortality ; Breast Neoplasms/surgery ; Computer Simulation ; Female ; Humans ; Length of Stay ; Markov Chains ; Models, Statistical ; Proportional Hazards Models ; Risk Assessment/methods ; Risk Factors ; Survival Analysis ; Time Factors
Language	English
Publishing date	2017-09-05
Publishing country	England
Document type	Journal Article
ZDB-ID	843037-8
ISSN	1097-0258 ; 0277-6715
ISSN (online)	1097-0258
ISSN	0277-6715
DOI	10.1002/sim.7448
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